I like Jason's idea (specifically real_nth_root) as a method.
However, to me the real issue is plotting. If someone tries to get a
cube root of -1 and gets a complex number, at least they see there is
an output! And then someone can help them understand why they get
that answer.
But there is a
On Thu, May 14, 2009 at 12:34 PM, Jason Grout wrote:
>> Bill Page wrote:
>> Ok thanks. I recall the discussion and I can indeed write:
>>
>> sage: f=lambda x:RR(x).nth_root(3)
>> sage: f(-2.0)
>> -1.25992104989487
>>
>> but I think I'll let my earlier comment stand:
>>
I think there should be
Bill Page wrote:
> On Thu, May 14, 2009 at 11:06 AM, Jason Grout wrote:
>> Bill Page wrote:
>>> Consider the problem to define
>>>
>>> f(x) = x^(1/3)
>>>
>>> so that it takes the real branch for x < 0. The best I have been able
>>> to come up with so far is:
>>>
>>> sage: f = lambda x:
>>> Rea
On Thu, May 14, 2009 at 11:06 AM, Jason Grout wrote:
>
> Bill Page wrote:
>>
>> Consider the problem to define
>>
>> f(x) = x^(1/3)
>>
>> so that it takes the real branch for x < 0. The best I have been able
>> to come up with so far is:
>>
>> sage: f = lambda x: RealField(53)(x).sign()*(RealFi
Bill Page wrote:
> On Thu, May 14, 2009 at 4:59 AM, John Cremona wrote:
>> This debate has been going on for as long as computers have been in
>> existence. Yes, there is a case to be made the odd roots of negative
>> reals should return a negative real instead of the "principal" complex
>> root.
On Thu, May 14, 2009 at 4:59 AM, John Cremona wrote:
>
> This debate has been going on for as long as computers have been in
> existence. Yes, there is a case to be made the odd roots of negative
> reals should return a negative real instead of the "principal" complex
> root. But that leads to m
On Thu, May 14, 2009 at 1:56 AM, Robert Bradshaw wrote:
>
> On May 13, 2009, at 9:11 PM, Bill Page wrote:
>
>> On Wed, May 13, 2009 at 11:54 PM, Robert Bradshaw wrote:
>>>
>>> This is because the branch in which the positive real root is real is
>>> taken. We're opting for continuity and consiste
This debate has been going on for as long as computers have been in
existence. Yes, there is a case to be made the odd roots of negative
reals should return a negative real instead of the "principal" complex
root. But that leads to more subtle problems in other places. If all
of mathematica, ma
On May 13, 2009, at 9:11 PM, Bill Page wrote:
> On Wed, May 13, 2009 at 11:54 PM, Robert Bradshaw wrote:
>>
>> This is because the branch in which the positive real root is real is
>> taken. We're opting for continuity and consistency with complex
>> numbers.
>>
>
> If I wrote:
>
> sage: Comple
On Wed, May 13, 2009 at 11:54 PM, Robert Bradshaw wrote:
>
> This is because the branch in which the positive real root is real is
> taken. We're opting for continuity and consistency with complex numbers.
>
If I wrote:
sage: ComplexField(53)(-2.0)^(1/3)
0.629960524947437 + 1.09112363597172*I
t
On May 13, 2009, at 8:49 PM, Bill Page wrote:
> On Wed, May 13, 2009 at 11:23 PM, Alex Ghitza wrote:
>>
>> On Thu, May 14, 2009 at 1:19 PM, Bill Page wrote:
>>>
>>> On Wed, May 13, 2009 at 10:46 PM, Mike Hansen wrote:
On Wed, May 13, 2009 at 6:58 PM, Bill Page wrote:
>
> Can som
On Wed, May 13, 2009 at 11:23 PM, Alex Ghitza wrote:
>
> On Thu, May 14, 2009 at 1:19 PM, Bill Page wrote:
>>
>> On Wed, May 13, 2009 at 10:46 PM, Mike Hansen wrote:
>>>
>>> On Wed, May 13, 2009 at 6:58 PM, Bill Page wrote:
Can someone explain this apparently inconsistent result?
>>>
>>>
On Thu, May 14, 2009 at 1:19 PM, Bill Page wrote:
>
> On Wed, May 13, 2009 at 10:46 PM, Mike Hansen wrote:
>>
>> On Wed, May 13, 2009 at 6:58 PM, Bill Page wrote:
>>>
>>> Can someone explain this apparently inconsistent result?
>>
>> It's just operator precedence:
>>
>> sage: -(2.0^(1/3))
>> -1.2
On Wed, May 13, 2009 at 10:46 PM, Mike Hansen wrote:
>
> On Wed, May 13, 2009 at 6:58 PM, Bill Page wrote:
>>
>> Can someone explain this apparently inconsistent result?
>
> It's just operator precedence:
>
> sage: -(2.0^(1/3))
> -1.25992104989487
> sage: (-2.0)^(1/3)
> 0.629960524947437 + 1.09112
On Wed, May 13, 2009 at 6:58 PM, Bill Page wrote:
>
> Can someone explain this apparently inconsistent result?
It's just operator precedence:
sage: -(2.0^(1/3))
-1.25992104989487
sage: (-2.0)^(1/3)
0.629960524947437 + 1.09112363597172*I
--Mike
--~--~-~--~~~---~--~-
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